when I am designing parts, I am never without the calculator.
...figuring diameters of circles and lengths of arcs is pretty simple once you get used to it.

another trick is literally moving and joining curved parts on the screen,
and moving them around to measure lengths and arcs.

This isn't that hard in 2D.

In your graphics program*, you should be able to rotate parts on the screen.
Once they are in rotation mode, look for a way to reposition the rotating center point of the part you are going to turn.
By positioning and repositioning that rotation point, you can butt parts together and rotate them around each other.
Allowing you to see where lines meet as the parts roll and rotate into position.

Of course there is no substitute for a test build of the actual parts to see how well things line up...but you can reduce the amount of adjustments necessary by simulating the connection in your 2D program.

*I'm trying to generalize methods and avoid detailed instructions as they apply to specific programs.
If everyone used one program...the same program...for all their graphics and design,
then it would be easy to swap and share instructions.
But what you can do in one program you might not be able to do in another.
And if you can do it, it might have different steps and tools to achieve the same result.